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allsm [11]
4 years ago
14

The hawaiian alphabet has 12 letters. How many permutations are possible for five of these letters

Mathematics
1 answer:
guajiro [1.7K]4 years ago
3 0

Answer: The answer is 50980

Step by Step Explanation:

First, temporarily assume that two letters with I are different, call them i 1 and i 2. Three "a" are also called as a 1, a 2 and a 3, and two h as h 1 and h 2. Then there are 11 * 10 * 9 * 8 * 7 = 55440 possible "words" (one of 11 is the first letter, 10 is the second, and so on). But because equal letters do the same "words," some "words" were counted twice or more. We have to deduct the number of "parasitic" counts although it is fairly small. The words that counted more than once are divided into many disjoint sets: 1) with two I but without repetitions of a and h; 2) with two h but without repetitions of a and I 3) with two a but without repetitions of I and h; 4) with three a but without repetitions of I and h; 5) with two I and two a's; 6) two i's and tree a's; 7) two i's and two h's 8) two h's and two a's; 9) two h's and one tree. The first category includes terms counted twice and its scale is (5 * 4) * (6 * 5 * 4) = 2400 (the first I stays at one of the 5 positions, the second at one of the 4, then 11-2i-1h-2a=6). So we have 2400/2 = 1200 to subtract. Group 2 gives -600 as well, and group 3 also. Group 4 gives * (6 * 5) = 1800 (5 * 4 * 3), and the terms are counted 6 times, -300. Groups 5, 7 , 8: 5 * 4 * 3 * 2 * 6 = 720 and counted four times, therefore -180. Group 6 and 9: 5 * 4 * 3 * 2 * 1 = 120, with 12 counts, -10. Altogether -(1200 * 3 + 300 + 180 * 3 + 10 * 2) = -4460.The answer will be 55440-4460 = 50980.

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The linear function that represent the cost per pound of the gummy bears in x years after 2000 is given by:

y(x) = 0.0425x + 0.38

<h3>What is a linear function?</h3>

A linear function is modeled by:

y = mx + b

In which:

  • m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.
  • b is the y-intercept, which is the value of y when x = 0, which can also be interpreted as the initial value of the function.

In this problem, we have that:

  • In 2000, Carl’s Candy Shop sold gummy bears for $0. 38 per pound, hence b = 0.38.
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Thus, the function is:

y(x) = 0.0425x + 0.38

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We have B number of bananas, each purchased at 10 cents.
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Answer:

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Step-by-step explanation:

Parallelograms can be said to be shapes which has four sides including two pairs of sides that are parallel and the four shapes are square, rectangle, rhombus, and rhomboid. Although rhombus is said to look exactly like a slanted square, while rhomboid is said to looks like a slanted rectangle.

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